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WASHINGTON — President Obama optimistically opened a 47-nation nuclear summit yesterday, boosted by Ukraine’s announcement that it will give up its weapons-grade uranium.

At the gathering, the United States and China said they would seek common ground on how to respond to Iran’s continued nuclear defiance.

Ukraine’s decision will help fulfill Obama’s goal of securing all vulnerable nuclear materials worldwide within four years, an objective that the White House hopes will be endorsed by all summit countries at a closing session today, even if the means to accomplish it are unclear.

The leaders are grappling with the possibility that terrorists or a nation other than the major nuclear powers could obtain crucial ingredients and inflict horrendous damage.

Obama and President Hu Jintao of China held a lengthy, one-on-one meeting before the summit opened. They said afterward that they would seek agreement on potential sanctions to discourage Iran’s efforts to come up with its own nuclear weapon.

Before the summit’s opening session and a working dinner, Obama held a series of meetings with leaders from Ukraine, China, Jordan, Armenia, and Malaysia. Presidential aides billed the summit as the largest gathering of world leaders hosted by a US president since the 1945 conference in San Francisco that founded the United Nations.

In a brief exchange with reporters at the White House, Obama said of the summit: “It’s impressive. I think it’s an indication of how deeply concerned everybody should be with the possibilities of nuclear traffic, and I think at the end of this we’re going to see some very specific, concrete actions that each nation is taking that will make the world a little bit safer.’’

The talks are a centerpiece of Obama’s broader agenda for ridding the world of nuclear weapons, a long-term process that he says should include gradual disarmament by the nuclear powers, stronger steps to head off a nuclear arms race, and more urgent action to lock down tons of plutonium and highly enriched uranium that are the key building blocks of atomic weapons.

According to Harvard’s Belfer Center, there are about 3.5 million pounds of highly enriched uranium and half a million pounds of bomb-grade plutonium in the world.

Combined, they could be used to build as many as 200,0000 nuclear weapons, or about 8.5 times the world’s current total of 23,360 warheads.

At a parallel, unofficial conference of more than 200 international nuclear experts, participants said too many leaders don’t share Obama’s urgency about nuclear ingredients.

“There is a great complacency among policymakers around the world that terrorist groups couldn’t make a nuclear bomb,’’ said Matthew Bunn of Harvard.

In a detailed report on the challenge of securing nuclear materials, Bunn said no one really knows the likelihood of nuclear terrorism.

“But the consequences of a terrorist nuclear blast would be so catastrophic that even a small chance is enough to justify urgent action to reduce the risk,’’ he wrote.

“The heart of a major city could be reduced to a smoldering radioactive ruin, leaving tens to hundreds of thousands of people dead,’’ he said.

Seeking to highlight the urgency of the threat posed by terrorists in pursuit of a nuclear bomb, John Brennan, the White House’s counterterrorism chief, told reporters that Al Qaeda is actively in search of the key ingredients for a bomb and the expertise to assemble it.

He said such an improvised device could be obtained through criminal gangs or by infiltrating nuclear labs in Pakistan or other nuclear nations.